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Nodal positioning analysis (NPA)—A numerical method for determining flow behavior of thermoplastic materials
Author(s) -
Echenagucia J.,
Fricke A. L.,
Hassler J. C.
Publication year - 1980
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760201112
Subject(s) - flow (mathematics) , mechanics , momentum (technical analysis) , materials science , position (finance) , node (physics) , finite difference , finite difference method , iterative method , mathematical analysis , mathematics , physics , mathematical optimization , acoustics , finance , economics
A finite difference method is presented for the solution of two dimensional flow problems in polymer processing. The method is applicable to narrow gaps of any shape and variable thickness. NPA was developed for analyzing the filling stage of the injection molding cycle, but it could be used in extrusion, blown film, and other polymer processing operations. In NPA the position of the flow front is calculated at the end of each time increment, and an axial node is placed at the newest location of the flow front. Each axial node is then divided into a determined number of radial nodes. The velocity and temperature profiles are obtained from the simultaneous solution of the momentum and energy equations. The use of finite differences transforms the continuity, momentum, and energy equations into a system of linear equations which can be solved by any direct or iterative technique. The procedure is repeated until axial nodes have been placed throughout the whole flow channel or until the flow front stops due to polymer solidification. The main advantage of this technique, when compared to the use of a fixed finite difference grid, is that computation time is saved by considering only nodes filled with the fluid. Empty nodes are not considered and corrections for partially filled nodes are not needed. No complications due to the parabolic‐shape of the flow front profile are introduced because the axial nodes are placed at average front locations determined by the average velocity at the particular time interval under consideration.